# Properties

 Label 255.2.a Level $255$ Weight $2$ Character orbit 255.a Rep. character $\chi_{255}(1,\cdot)$ Character field $\Q$ Dimension $11$ Newform subspaces $4$ Sturm bound $72$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$255 = 3 \cdot 5 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 255.a (trivial) Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$72$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(255))$$.

Total New Old
Modular forms 40 11 29
Cusp forms 33 11 22
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$3$$$$5$$$$17$$FrickeDim.
$$+$$$$+$$$$-$$$$-$$$$2$$
$$+$$$$-$$$$+$$$$-$$$$2$$
$$-$$$$+$$$$+$$$$-$$$$4$$
$$-$$$$-$$$$-$$$$-$$$$3$$
Plus space$$+$$$$0$$
Minus space$$-$$$$11$$

## Trace form

 $$11q + 5q^{2} + 3q^{3} + 17q^{4} - q^{5} - 3q^{6} + 8q^{7} + 9q^{8} + 11q^{9} + O(q^{10})$$ $$11q + 5q^{2} + 3q^{3} + 17q^{4} - q^{5} - 3q^{6} + 8q^{7} + 9q^{8} + 11q^{9} + q^{10} + 12q^{11} + 5q^{12} + 2q^{13} - 8q^{14} - q^{15} + 17q^{16} - q^{17} + 5q^{18} - 4q^{19} - 7q^{20} + 8q^{21} - 12q^{22} + 8q^{23} - 15q^{24} + 11q^{25} - 18q^{26} + 3q^{27} - 8q^{28} + 2q^{29} - 3q^{30} - 8q^{31} - 7q^{32} - 12q^{33} - 3q^{34} + 17q^{36} + 26q^{37} - 28q^{38} + 2q^{39} - 3q^{40} + 6q^{41} - 24q^{42} - 4q^{43} - 12q^{44} - q^{45} - 32q^{46} - 16q^{47} - 3q^{48} + 27q^{49} + 5q^{50} - q^{51} - 58q^{52} + 10q^{53} - 3q^{54} - 12q^{55} - 72q^{56} + 28q^{57} - 34q^{58} - 20q^{59} - 7q^{60} - 14q^{61} - 64q^{62} + 8q^{63} - 19q^{64} + 18q^{65} - 8q^{66} - 4q^{67} - 7q^{68} - 16q^{69} - 12q^{70} + 9q^{72} + 38q^{73} - 10q^{74} + 3q^{75} - 8q^{76} + 6q^{78} - 16q^{79} + q^{80} + 11q^{81} - 6q^{82} - 4q^{83} - 4q^{84} + 3q^{85} + 44q^{86} - 6q^{87} - 12q^{88} + 38q^{89} + q^{90} - 8q^{91} + 56q^{92} + 24q^{93} + 20q^{94} - 20q^{95} - 23q^{96} + 30q^{97} + 61q^{98} + 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(255))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 3 5 17
255.2.a.a $$2$$ $$2.036$$ $$\Q(\sqrt{13})$$ None $$1$$ $$-2$$ $$-2$$ $$0$$ $$+$$ $$+$$ $$-$$ $$q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$$
255.2.a.b $$2$$ $$2.036$$ $$\Q(\sqrt{5})$$ None $$3$$ $$-2$$ $$2$$ $$0$$ $$+$$ $$-$$ $$+$$ $$q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$$
255.2.a.c $$3$$ $$2.036$$ 3.3.229.1 None $$0$$ $$3$$ $$3$$ $$4$$ $$-$$ $$-$$ $$-$$ $$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$$
255.2.a.d $$4$$ $$2.036$$ 4.4.13768.1 None $$1$$ $$4$$ $$-4$$ $$4$$ $$-$$ $$+$$ $$+$$ $$q-\beta _{3}q^{2}+q^{3}+(2-\beta _{1})q^{4}-q^{5}-\beta _{3}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(255))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(255)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(15))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(17))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(51))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_0(85))$$$$^{\oplus 2}$$